Related papers: Critical Phenomena: An Introduction from a modern …
Emergence is a profound subject that straddles many scientific disciplines, including the formation of galaxies and how consciousness arises from the collective activity of neurons. Despite the broad interest that exists on this concept,…
A relation between geometric phases and criticality of spin chains are studied by using the quantum renormalization-group approach. We have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size…
Meta-analysis, by synthesizing effect estimates from multiple studies conducted in diverse settings, stands at the top of the evidence hierarchy in clinical research. Yet, conventional approaches based on fixed- or random-effects models…
These two lectures cover some of the advances that underpin recent progress in deriving continuum solutions from the exact renormalization group. We concentrate on concepts and on exact non-perturbative statements, but in the process will…
These notes provide a concise introduction to important applications of the renormalization group (RG) in statistical physics. After reviewing the scaling approach and Ginzburg-Landau theory for critical phenomena, Wilson's momentum shell…
The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any…
Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…
Human interactions can be either positive or negative, giving rise to different complex social or anti-social phenomena. The dynamics of these interactions often lead to certain spatio-temporal patterns and complex networks, which can be…
Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…
Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
Scientific progress is inherently sequential: collective knowledge is updated as new studies enter the literature. We propose the sequential meta-analysis research trace (SMART), which quantifies the influence of each study at the time it…
It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from…
A reliable understanding of the Earth system is essential for the life quality of modern society. Natural hazards are the cause of most life and resource losses. The ability to define the conditions for a sustainable development of…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
The steady state shock formation in processes like nonconserving asymmetric simple exclusion processes in varied situations is shown to be a nonequilibrium critical phenomenon. The diverging length scales and the quantitative description of…
Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous…
The concept of emergence is critically analyzed in particular with respect to the assumed emergence of mental properties from a neuronal basis. We argue that so-called contextual emergence is needed to avoid an eliminatory reductionism.…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…